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An algorithm for the resource constrained shortest path problem
Abstract
In this paper we examine an integer programming formulation of the resource constrained shortest path problem. This is the problem of a traveller with a budget of various resources who has to reach a given destination as quickly as possible within the resource constraints imposed by his budget. A lagrangean relaxation of the integer programming formulation of the problem into a minimum cost network flow problem (which in certain circumstances reduces to an unconstrained shortest path problem) is developed which provides a lower bound for use in a tree search procedure. Problem reduction tests based on both the original problem and this lagrangean relaxation are given. Computational results are presented for the solution of problems involving up to 500 vertices, 5000 arcs, and 10 resources.
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Citations
Cited by
A survey of resource constrained shortest path problems: Exact solution approaches
Pugliese, L. D. P., & Guerriero, F. (2013) · Networks · doi:10.1002/net.21511 · Cited by 147
Resource Constrained Shortest Paths
Mehlhorn, K., & Ziegelmann, M. (2000) · Lecture Notes in Computer Science · doi:10.1007/3-540-45253-2_30 · Cited by 124
A technical review of column generation in integer programming
Wilhelm, W. E. (2001) · Optimization and Engineering · doi:10.1023/a:1013141227104 · Cited by 108
Metadata
- Authors
- Beasley, J. E., & Christofides, N.
- Venue
- Networks
- Publisher
- Wiley
- Published
- 1989-07
- Volume
- 19
- Issue
- 4
- Pages
- 379-394
- ISSN
- 0028-3045 (ISSN-L)
- 1097-0037
- OpenAlex
- W2130679277
- Cited by
- 327
- References
- 0
- FWCI
- 1.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: An algorithm for the resource constrained shortest path problem. https://app.cochat.ai/papers/10.1002/net.3230190402
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- Beasley, J. E., & Christofides, N. (1989). An algorithm for the resource constrained shortest path problem. Networks. https://doi.org/10.1002/net.3230190402
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